Multivariate Sobel-Uppuluri-Galambos-type bounds
E. Seneta and T. Chen
Research Report 99-17
Date: 2 August 1999
The upper and lower bounds in a recent multivariate generalization (Galambos
and Xu,1996) of the univariate Sobel-Uppuluri-Galambos inequalities are shown
to be weighted averages of individual multivariate bounds, and hence can be
sharpened by optimizing over these individual bounds. Examples are used to
illustrate the difference between bounds of this kind, and the kind of
multivariate bounds appearing in Chen and Seneta(1996) and Galambos and Lee
(1994). The difference in kind turns on the nature of extension of the idea
of degree from univariate to multivariate.
Bonferroni-type inequality. degree. Meyer's identity. multivariate.
optimization. weighted average.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics